The failure of consumption based asset pricing models to match the
stochastic properties of the equity premium and the risk-free rate has
been attributed by some authors to frictions, transaction costs or
durability. However, such frictions would primarily affect the higher
frequency data components: consumption-based pricing models that
concentrate on long-horizon returns should be more successful.

We consider two consumption-based models: time-separable utility, and
the habit model of Constantinides (1990). We estimate a vector
ARCH model that includes the pricing kernel and the equity return, and
use the fitted model to assess the model's implications for the equity
premium and for the risk-free rate. Neither model performs well at a
quarterly horizon, but at longer horizons the Constantinides model can
match the mean and the variance of the observed equity premium,
captures time-variation of the equity premium, and can better match
the observed risk-free rate. We conclude that the equity premium and
risk-free rate puzzles are primarily problems for shorter-horizon
returns.